As a general matter, CAD systems require a constraint server for geometric modeling purposes. Most conventional CAD CS's are parametric with some limited variational capabilities. Several geometric problems are not easily solved with parametric methods, so designers and users of conventional constraint servers attempt to adapt them to solve these modeling problems on a special-case basis.
The special cases employ methods that are somewhat variational, but not in a broad sense of the term. Instead, the adapted functionality is somewhat analogous to the goal seeking capability of a spreadsheet. A spreadsheet is basically parametric, but with a limited ability to solve systems of equations through the use of goal seeking methods.
As a general matter, CAD systems use a parametric, feature-based representation of the solid model. Features are parametric shapes defined by intrinsic geometric parameters, position, and orientation. The user designs a part by incrementally adding features to a solid body. Some CAD systems currently also employ a direct-modeling interface, which allows users to directly move surfaces without any information about part features.